Methods and apparatus for generating a sinusoidal motor drive signal for a MEMS gyroscope

ABSTRACT

An apparatus is described which reduces a time delay and a resultant phase shift in a gyroscope motor drive signal. The motor drive signal originates from a numerically controlled oscillator whose output is sampled at a predetermined rate. The apparatus includes a first element which upsamples the oscillator output signal samples and a band pass filter configured to receive an output from the first element and remove spectral components from the output of the first element. The apparatus further includes a third element which generates a tuning parameter, β o ′, for tuning of the band pass filter and a scaling multiplier configured to normalize an output of the filter.

BACKGROUND OF THE INVENTION

[0001] This invention relates generally to digital signal processing(DSP) and, more specifically, to methods and apparatus for generatingmotor drive signals for micro-electromechanical system (MEMS)gyroscopes.

[0002] To provide a motor drive signal for MEMS gyroscopes, a digitalsinusoidal signal of frequency f_(o) is generated by a numericallycontrolled dual-frequency oscillator (NCDFO). A command input to theoscillator is β_(o)=cos(2πf_(o)T), where f_(s)=1/T is a clock frequencyof the oscillator. The frequency f_(o) varies with changes in β_(o). Thedigital sinusoidal signal serves as the input to a drive circuit which,in turn, provides an analog signal to a gyroscope drive motor. Becausethe above described gyroscope motor drive configuration is within aclosed-loop control system, the destabilizing effect of time delay, andan attendant phase shift resulting from the time delay, will cause anoperational issue to result.

[0003] One known attempted solution is to pass the NCDFO output signalthrough a digital-to-analog converter (DAC), whose output is passedthrough a low pass, anti-aliasing filter to smooth the analog gyro-drivesignal. Unfortunately, the time delay introduced by the combination ofthese operations is too long to permit solid closed-loop operation. Adigital-to-analog-conversion scheme with lower phase shift is clearlyneeded.

BRIEF SUMMARY OF THE INVENTION

[0004] In one aspect, an apparatus to reduce a time delay and aresultant phase shift in a gyroscope motor drive signal is provided. Themotor drive signal originates from a numerically controlled oscillator,the oscillator output being sampled at a predetermined rate. Theapparatus comprises a first element which upsamples the oscillatoroutput signal samples, a band pass filter configured to receive anoutput from the first element and remove spectral components of theoutput of the first element, a third element which generates a tuningparameter, β_(o)′, to tune the band pass filter, and a scalingmultiplier configured to normalize an output of the filter.

[0005] In another aspect, a method for reducing a time delay and aresultant phase shift in a gyroscope motor drive signal which originatesfrom a numerically controlled oscillator is provided. The methodcomprises placing I−1 zero value samples between each pair of oscillatoroutput samples, filtering spectral components from the combinedoscillator output samples and zero value samples, generating a tuningparameter, β_(o)′, for use in filtering, and scaling a filter ouput.

[0006] In still another aspect, an angular rate measurement system isprovided. The system comprises a gyroscope configured to sense anangular rate input and provide a modulated angular rate informationsignal and a sinusoidal demodulation reference signal. The system alsocomprises a numerically controlled oscillator (NCO) configured toreceive as an input a tuning parameter β, which is a digitized signalderived from the sinusoidal demodulation reference signal. The NCO isfurther configured to provide output samples. The system also comprisesan automatic gain control (AGC) circuit configured to amplify the outputsamples of the NCO, an interpolator, and a digital-to-analog converterand filter configured to produce a motor drive signal from an output ofthe interpolator. The interpolator is configured to place I−1 zero valuesamples between each pair of amplified output samples, and theinterpolator comprises a filter configured to filter spectral componentsfrom the combined amplified output samples and zero value samples. Theinterpolator further generates a tuning parameter, β_(o)′, for thefilter, and scales the filtered samples to be output from theinterpolator.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007]FIG. 1 illustrates a gyroscope angular rate sensing systemincluding an interpolator circuit for reducing a time delay ingenerating a gyro motor drive signal.

[0008]FIG. 2 illustrates an embodiment of an interpolator circuit usedin the angular rate sensing system of FIG. 1.

DETAILED DESCRIPTION OF THE INVENTION

[0009] Referring to FIG. 1, an angular rate measurement system 10 asshown is built around gyroscope 20 which senses input angular rate 22. Afirst output 24 of gyroscope 20 is an electrical signal which is adouble side band suppressed carrier (DSSC) modulated representation, ata fundamental frequency 2f_(o), of the input angular rate 22. Firstoutput 24 is input to an analog-to-digital conversion (ADC) system 26including an internal analog anti-alias filter, a sampler, and adigitizer (none shown). An output 28 from ADC system 26 is input to anddemodulated by demodulator 30 which, as further described below,receives demodulating signals from numerically controlled dual frequencyoscillator (NCDFO) 32. An output 34 from demodulator 30 is filtered withfilter 36 whose output 38 is a base band digitized representation ofangular input rate 22.

[0010] Gyroscope 20 provides a second output 40, which is a sinusoidaldemodulation reference signal at a frequency 2f_(o). Second output 40 isconnected to a second ADC system 42, functionally identical to ADCsystem 26. An output 44 from ADC 42 is then input to both a phasedetector/servo equalizer 46 and an automatic gain control (AGC) 48.Phase detector/servo equalizer 46 is a combination fast-acting automaticgain control, phase shifter, phase detector, and servo equalizer. Anoutput 50 of phase detector/servo equalizer 46 is a tuning parameterβ_(o)=cos(2πf_(o)T) which determines the frequency of oscillation ofNCDFO 32 (NCDFO 32 has a clock rate of 1/T) and is connected to a firstinput 52 of NCDFO 32. NCDFO 32 provides two outputs 54 and 56 inquadrature at frequency 2f_(o) and another pair of outputs in quadratureat frequency f_(o). In the embodiment shown, only one output 60 isconnected to an input 62 of automatic-gain control (AGC) 48.

[0011] As stated above, output signal 44 from ADC 42 is connected to asecond input 64 of AGC 48. Output signal 66 from AGC 48 is an amplifiedversion of oscillator output 60, and is automatically adjusted inamplitude until the amplitude of signal 64 reaches a predeterminedlevel. Signal 66 is connected to an input 68 of interpolator 70, whichis described in further detail below. Output 72 of NCDFO 32 is thesquare of tuning parameters β_(o) and is connected to a second input 74of interpolator 70. Input signal 68 to interpolator 70 is a sinusoid ofprescribed amplitude, frequency f_(o), and sampling frequency f_(s).Output signal 76 from interpolator 70 is a sinusoid of the sameamplitude and frequency as input signal 68, but at a sampling frequencyof I·f_(s), as interpolator 70 increases a sampling rate of input signal68 by a factor of I. Output signal 76 from interpolator 70 is connectedto an input 78 of a signal conditioning element 80, whose output 82 isinput to a digital-to-analog converter (DAC) and filter 84. An output 86of DAC and filter 84 is input to an analog driver 88 which produces amotor-drive signal 90 for gyroscope 20.

[0012]FIG. 2 is a block diagram of interpolator 70 including fourelements. A first element upsamples an output signal from oscillator 32(shown in FIG. 1) by placing I−1 values of zero between each pair ofsamples from oscillator 32. The upsampled signal drives the secondelement, a Gray-Markel, lattice-based, second order, band passinterpolation filter, which is clocked at a frequency of I/T to removeall extraneous spectral components of the upsampled signal. As furtherdescribed below, a passband-width parameter, α, in a preferredembodiment, is set to 0.999 and a tuning parameter of the filter is setto β_(o)′=cos(2πf_(o)T/I)=cos[1/I cos⁻¹(β_(o))]. The third element tunesthe filter by generating the filter tuning parameter β_(o)′, via a threeterm power series where, β_(o)′≈a₀+a₁β_(o) ²+a₂β_(o) ⁴. The term β₀ ²,is provided by oscillator 32. A fourth element of interpolator 70 is ascaling multiplier which renormalizes the signal amplitude by a factorof I/2.

[0013] Referring specifically to Fi,ure 2, interpolator 70 includes athree-input second-order band pass filter 100 and a power seriescalculation section 102. In the embodiment shown, band pass filter 100is a Gray-Markel single-multiplier per order all pass structure whoseoutput 104 is subtracted from an input 106 to provide band passfiltering. Input 106 is delivered to band pass filter 100 by samplingfunction 108. Output 110 from band pass filter 100 is scaled by I/2 inmultiplier 112 to generate output signal 76.

[0014] Input 106 is connected to an additive input 114 of a firstsubtraction element 116, an additive input 118 of a second subtractionelement 120, and a first input 122 of a first adder 124. Output 126 offirst adder 124 is connected to a first input 128 of a first multiplier130. A second input 132 to first multiplier 130 is α, an externallysupplied parameter. In a specific embodiment, α is set to a value of0.999. An output 134 of first multiplier 130 is connected to asubtractive input 136 of first subtraction element 116 and a first input138 of second adder 140. Output 104 of second adder 140 is connected toa subtractive input 142 of second subtraction element 120.

[0015] Output 150 of first subtraction element 116 is connected to anadditive input 152 of third subtraction element 154 and to an additiveinput 156 of fourth subtraction element 158. A first input 160 of secondmultiplier 162 is connected to an output 164 of third subtractionelement 154. A second input 166 to second multiplier 162 is β_(o)′,which is a tuning parameter for band pass filter 100. An output 168 ofsecond multiplier 162 is connected to a subtractive input 170 of thirdsubtraction element 158 and a subtractive input 172 of a fifthsubtraction element 174.

[0016] An output 176 of fourth subtraction element 158 is connected to afirst delay element 178. An output 180 of first delay element 178 isconnected to a subtractive input 182 of third subtraction element 154and to an additive input 184 of fifth subtraction element 174. An output186 of fifth subtraction element 174 is connected to an input 188 ofsecond delay element 190. Output 192 of second delay element 190 isconnected to a second input 194 of first adder 124 and a second input196 of second adder 140.

[0017] In operation, a sinusoid at a frequency f_(o), is provided atinput 68 at a sampling frequency of f_(s), to sampling function 108. Thesinusoid at input 68 is modified at sampling function 108 by insertionof I−1 values of zero being input between each pair of input samples ofthe sinusoid. A new signal is created at a sampling rate of I·f_(s). Asdescribed above, band pass filter 100 has as its second input 132 theparameter α, that determines a bandwidth for band pass filter 100. Thebandwidth parameter, α, has, in one embodiment, a nominal value of0.999, where α is determined as α=tan(πf_(BW)T/I), and where f_(BW) isthe 3 dB bandwidth (in Hz) of the pass band. A center of the pass bandis tuned by input 166, the parameter β_(o)′, where${\beta_{o}^{\prime} = {{\cos \left( {2\pi \quad f_{o}{T/I}} \right)} = {\cos \left\lbrack {\frac{1}{I}{\cos^{- 1}\left( \beta_{o} \right)}} \right\rbrack}}},$

[0018] where β_(o) is the input to NCDFO 32.

[0019] Direct calculation of β_(o)′, from β_(o) is difficult, but aChebychev approximation can be obtained, in one embodiment, by athree-term power series, for example, β_(o)′≈a₀+a₁β_(o) ²+a₂β_(o) ⁴.This power series is mechanized in power series calculation section 102whose input 74, β₀ ², is obtained directly from NCDFO 32. Input 74 isconnected as a first input to third multiplier 200 and fourth multiplier202. A second input 204 of third multiplier 200 is coefficient a₂. Anoutput 206 of third multiplier 200 is summed with coefficient a₁, inthird adder 208, whose output 210 is connected to a second input 212 offourth multiplier 202. Fourth adder 214 sums an output 216 of multiplier202 with coefficient a₀. An output 218 of adder 214 is the tuningparameter β_(o)′. In one embodiment, a₀, a₁, and a₂, are computedutilizing a Chebychev approximation program as illustrated in AppendixA. In a specific embodiment, and as outlined in Appendix A, a₀ is0.9967032511, a₁ is 0.00526891, and a₂ is −0.0021640344.

[0020] Numerically controlled, dual frequency oscillators (NCDFO)implemented in MEMS gyroscope motor drive systems, typically produce asinusoid, whose frequency may not be constant, and which is sparselysampled. Such a motor drive system can introduce an unacceptable amountof time delay and phase shift, as above described. One way to improveperformance of such motor drive systems is to increase the samplingfrequency of the NCDFO output signal through the use of interpolator 70.Implementation of system 10, including interpolator 70 allows anincrease in the sampling frequency of the NCDFO output signal by afactor of I, where I is greater than one, and typically eight or more.The combined time delay of interpolator 70, a higher frequency DAC, anda simple low pass, anti-aliasing filter (DAC and filter 84) is less thanthe time delays in known gyroscope motor drive systems.

[0021] While the invention has been described in terms of variousspecific embodiments, those skilled in the art will recognize that theinvention can be practiced with modification within the spirit and scopeof the claims.

What is claimed is:
 1. An apparatus to reduce a time delay and a resultant phase shift in a gyroscope motor drive signal, the motor drive signal originating from a numerically controlled oscillator having an output, the oscillator output being sampled at a predetermined rate, said apparatus comprising: a first element which upsamples the oscillator output samples; a band pass filter configured to receive an output from said first element and remove spectral components of the output of said first element; a third element which generates a tuning parameter, β_(o)′, to tune said band pass filter; and a scaling multiplier configured to normalize an output of said filter.
 2. An apparatus according to claim 1 wherein said first element is configured to upsample the oscillator output by a factor of I by placing I−1 values of zero samples between each pair of samples received from the oscillator.
 3. An apparatus according to claim 1 wherein I has a value greater than one.
 4. An apparatus according to claim 1 wherein I has a value from eight to sixteen.
 5. An apparatus according to claim 1 wherein said band pass filter comprises a Gray-Markel lattice-based, second order band pass interpolation filter, clocked at a frequency of I/T, where 1/T is a clock rate of the oscillator.
 6. An apparatus according to claim 5 wherein said band pass filter comprises an input parameter α, for determining a bandwidth for said band pass filter, where α has a nominal value of 0.999.
 7. An apparatus according to claim 5 wherein said band pass filter comprises an input parameter α which is determined as α=tan(πf_(BW)T/I), and where f_(BW) is a 3 dB bandwidth (in Hz) of the pass band.
 8. An apparatus according to claim 5 wherein a tuning parameter for the pass band of said filter is ${\beta_{o}^{\prime} = {{\cos \left( {2\pi \quad f_{o}{T/I}} \right)} = {\cos \left\lbrack {\frac{1}{I}{\cos^{- 1}\left( \beta_{o} \right)}} \right\rbrack}}},$

where β_(o) is an input to the oscillator.
 9. An apparatus according to claim 1 wherein the tuning parameter, β_(o)′, is set to β_(o)′≈a₀+a₁β_(o) ²+a₂β_(o) ⁴, where the term β₀ ², is provided by the oscillator.
 10. An apparatus according to claim 1 wherein said scaling multiplier has a value of I/2.
 11. A method for reducing a time delay and a resultant phase shift in a gyroscope motor drive signal which originates from a numerically controlled oscillator, said method comprising: placing I−1 zero value samples between each pair of oscillator output samples; filtering spectral components from the combined oscillator output samples and zero value samples; generating a tuning parameter, β_(o)′, for said filtering; and scaling an output of said filtering.
 12. A method according to claim 11 wherein I has a value greater than one.
 13. A method according to claim 11 wherein I has a value from eight to sixteen.
 14. A method according to claim 11 wherein said filtering comprises filtering with a Gray-Markel lattice-based, second order band pass interpolation filter, clocked at a frequency of I/T, where 1/T is a clock rate of the oscillator.
 15. A method according to claim 14 further comprising: providing an input parameter, α, to the filter which has a nominal value of 0.999; and determining a bandwidth for the band pass filter using the input parameter.
 16. A method according to claim 14 further comprising providing an input parameter, α, to the filter which is determined as α=tan(πf_(BW)T/I), and where f_(BW) is a 3 dB bandwidth (in Hz) of the pass band.
 17. A method according to claim 14 further comprising providing a tuning parameter for the pass band of the band pass filter, the tuning parameter calculated as ${\beta_{o}^{\prime} = {{\cos \left( {2\pi \quad f_{o}{T/I}} \right)} = {\cos \left\lbrack {\frac{1}{I}{\cos^{- 1}\left( \beta_{o} \right)}} \right\rbrack}}},$

where β_(o) is an input to the oscillator.
 18. A method according to claim 14 further comprising determining the tuning parameter, β_(o)′, using a power series, where β_(o)′≈a₀+a₁β_(o) ²+a₂β_(o) ⁴, where the term β₀ ², is provided by the oscillator.
 19. A method according to claim 11 wherein said scaling an output of said filtering comprises providing a scaling multiplier with a value of I/2.
 20. An angular rate measurement system comprising: a gyroscope configured to sense an angular rate Input and provide a modulated angular rate information signal and a sinusoidal demodulation reference signal; a numerically controlled oscillator (NCO) configured to receive as an input a tuning parameter β, which is a digitized signal derived from the sinusoidal demodulation reference signal, said oscillator further configured to provide output samples; an automatic gain control (AGC) circuit configured to amplify the output samples of said NCO; an interpolator configured to place I−1 zero value samples between each pair of amplified output samples, said interpolator comprising a filter configured to filter extraneous spectral components from the combined amplified output samples and zero value samples, generate a tuning parameter, β_(o)′, for said filter, and scale the filtered samples to be output from said interpolator; and a digital-to-analog converter and filter, said converter and filter configured to produce a motor drive signal from an output of said interpolator.
 21. An angular rate measurement system according to claim 20 wherein I ranges from eight to sixteen.
 22. An angular rate measurement system according to claim 20 wherein said interpolator comprises a Gray-Markel lattice-based, second order band pass interpolation filter, clocked at a frequency of I/T, where 1/T is a clock rate of said NCO.
 23. An angular rate measurement system according to claim 20 wherein an input parameter to said interpolator, α, is determined according to α=tan(πf_(BW)T/I), and where f_(BW) is a 3 dB bandwidth (in Hz) of a pass band for said filter.
 24. An angular rate measurement system according to claim 20 wherein a tuning parameter for a pass band for said filter is calculated as ${\beta_{o}^{\prime} = {{\cos \left( {2\pi \quad f_{o}{T/I}} \right)} = {\cos \left\lbrack {\frac{1}{I}{\cos^{- 1}\left( \beta_{o} \right)}} \right\rbrack}}},$

where β_(o) is an input to said NCO.
 25. An angular rate measurement system according to claim 20 wherein said interpolator is configured to approximate a tuning parameter, β_(o)′, for said filter using a power series, where β_(o)′≈a₀+a₁β_(o) ²+a₂β_(o) ⁴, where the term β₀ ², is provided by said oscillator.
 26. An angular rate measurement system according to claim 25 wherein a₀ is 0.9967032511, a₁ is 0.00526891, and a₂ is −0.0021640344. 